The present invention relates to a three-phase induction motor and, more particularly, to a three-phase induction motor having a relatively small capacity (e.g., an output of 1 kW or less) and aiming at torque smoothing.
Three-phase induction motors have been widely applied in general industrial machines such as various machine tools since constant speeds can be obtained when the motors are simply connected to three-phase power sources.
The torque T of a three-phase induction motor is given by the following equation: EQU T=M(-jI.sub.1)I.sub.2
where M is the mutual inductance between the primary and secondary windings, -jI.sub.1 is the primary current (stator current) vector, and I.sub.2 is the secondary current (rotor current) vector.
In order to smooth the torque of the three-phase induction motor, positional variations in the mutual inductance M and harmonic components of the primary and secondary current vectors I.sub.1 and I.sub.2 must be eliminated. The primary current vector I.sub.1 is determined by a power source waveform and cannot be improved in the induction motor. However, there is much room to improve the mutual inductance M and the harmonic components based on the second current vector I.sub.2.
The number N of slots formed in the stator of the three-phase induction motor is determined by: EQU N=(number l of poles).times.(number m of phases) .times.(number q of slots per pale per phase)
In a conventional induction motor, since a stator winding can be easily and uniformly wound, the stator is designed such that the number q of slots is an integer. For this reason, positional variations in the mutual inductance M and the harmonic influence of the secondary current vector I.sub.2 cannot be eliminated.
FIGS. 1(a) to 1(e) explain the mutual inductance M in the prior art. FIG. 1(a) shows positions of stator slots when the number of poles, is 2, the number of phases are 3, and the number of slots per pole per phase is 2, i.e., the total number of slots is 12. FIG. 1(b) is a developed view of the disposition of slots in FIG. 1(a) FIG. 1(c) shows variations in magnetic flux in the air gaps corresponding in position to the slots and FIG. 1(d) shows an S-pole slot disposition corresponding to the N-pole slot disposition and magnetic flux variations of the S pole. In other words, FIG. 1(d) is obtained by shifting the portions included in the S pole in FIGS. 1(b) and 1(c) in a direction indicated by arrow A. FIG. 1(e) shows variations in the mutual inductance M caused by a combination of the N- and S-pole magnetic flux variations. As shown in FIG. 1(e), variations in the mutual inductance M are large cause variations in torque T, thus interfering with smooth rotation of the induction motor.
It is desirable to obtain a sinusoidal magnetic flux distribution in the gap between the stator and the rotor. However, in practice, the magnetic flux distribution is not sinusoidal but stepwise because a wire is wound around the core of the stator to fill the slots. Therefore, the stepwise waveform includes a plurality of harmonic components. The harmonic components cause undesirable phenomena such as generation of a torque ripple, noise, vibrations, and a temperature rise. The harmonic components have a larger number of steps when the number of slots per pole per phase in the stator is increased. The increase in the number of steps makes it possible to provide a substantially sinusoidal waveform. For this reason, the number of slots can be increased in a large motor, but it cannot be increased over a certain limitation. An rth order harmonic voltage Er induced in the secondary winding is expressed as follows: EQU Er .varies..phi..times.Kd.times.Kp (1)
where .phi. is the magnetic flux, Kd is the distribution coefficient, and Kp is the short node winding coefficient if a pitch s of the stator winding is defined as s=(r-t)/r or the long node winding coefficient if the pitch s is defined as s=r/r+t (where t is an odd number). The coefficients Kd and Kp for t=1 are given by: EQU Kd={sin(r.pi./2m)}/{qsin(r.pi./2mq)} (2)
where r is the harmonic order, m is the number of phases, and q is the number of slots per pole and phase. EQU Kp={sinrr.pi./2.multidot.sin(rW.pi./2.tau.)} (3)
where w is the coil pitch represented by the number of slots, and .tau. is the number of slots per pole.
Since the coefficients Kd and Kp are determined by the pitch S of the stator winding, i.e., the slot positions, predetermined harmonic components cannot be eliminated.
A conventional compact induction motor, therefore, tends to generate a torque ripple. If such a motor is used as a servo drive source in a machine tool or an industrial robot, various problems result. More specifically, in the case of a machine tool, a blade cannot be smoothly driven and the cut surface is roughened. In the case of a robot, its arm cannot be moved smoothly.